The wealth lower bound can be viewed as a discrete mixture, which is called a hedged betting in [1]}, over two continuous mixture wealth processes.
Here, the first term \(Z_n(\mathbf {\rho }_n(y^t;m),\eta _{n}(y^t;m))\)  corresponds to the mixture of constant bettors \(b\in [m,1)\)  and the second term corresponds to \(b\in (0,m]\) , and they are weighted by \((1-m)\)  and \(m\) , respectively.
